Also lending their support are both the Christian Institute and the National Secular Society.
The National Secular Society, meanwhile, urged the prime minister to "ignore Lord Carey's theocratic and anti-democratic blustering".
The move has been welcomed by the National Secular Society which said the current system was discriminatory.
The National Secular Society said Bishop Pritchard's comments were a "step in the right direction" but expressed doubt about whether changes would be made.
Terry Sanderson, president of the National Secular Society, says the fall in the number of Christians showed a "huge upheaval" in attitudes towards religion.
"The reason these books are proving popular is that religion is becoming center stage, " said Keith Porteous Wood, director of the National Secular Society.
The National Secular Society, which campaigns for the separation of religion from education, is critical of the need for parental consent for pupils to withdraw from the worship.
Keith Porteous Wood, executive director of the National Secular Society, said the future of equality legislation in Britain - and even Europe - could depend on the ruling.
"I saw an interview recently with the singer, Neil Diamond, who isn't actually Christian, he's Jewish, " says Alistair McBay, who is spokesman for the National Secular Society in Scotland.
The National Secular Society (NSS) said it would mount a protest campaign made up of gay groups, victims of clerical abuse, feminists, family planning organisations and pro-abortion groups, among others.
But critics such as the National Secular Society say the attorney-general's role may be one of most dangerous things of all, because it ensures the decision to prosecute will be political.
The National Secular Society welcomed the charity regulator's ruling.
In March, the National Secular Society, which aims to restrict the role of religion in public life, wrote to Chief Scout Bear Grylls, complaining that atheist children were being excluded or having to lie to join the movement.
But Terry Sanderson, president of the National Secular Society, accused Mr Pickles - who cited recent action to allow councils to hold prayers at the start of meetings in the wake of a High Court ruling - of trying to restore "sectarianism".
The secular National Democratic Action Society is Bahrain's main leftist political society, is running after boycotting the previous elections.
"Robbie stepped aside because he signed up as president to organise events and run a student society, " said Michael Paynter, secretary for the National Federation of Atheist, Humanist and Secular Student Societies.
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